Detectable Electric Current induced by Dark Matter Axion in a Conductor

Abstract: We propose a way of detecting dark matter axion by using two slabs of conductor. The flat surfaces are put to meet face to face so that they are parallel to each other. External magnetic field $B$ parallel to the surfaces is impressed. Radiations converted from the axion arise between two slabs. When we tune the spacing $l$ between two surfaces such as $l=\pi/m_a$ with axion mass $m_a$, a resonance occurs so that the radiations become strong. Furthermore, electric current flowing on the surface of the slabs is enhanced. We show that the electric current is large enough to be detectable at the resonance. It reaches $0.7\times 10^{-9}$A$(10^{-5}\mbox{eV}/m_a)^{1/2}(B/5\mbox{T})(L/10\mbox{cm})(\sigma/3.3\times 10^7\rm eV)$, using $6$N copper of the square slab with side length $L$ and high electrical conductivity $\sigma$ at temperature $T\sim 1$K. The power of the Joule heating is $0.3\times10^{-22}\mbox{W}(B/5\mbox{T})^2(10^{-5}\mbox{eV}/m_a)^{1/2}(L/10\mbox{cm})^2(\sigma/3.3\times 10^7\rm eV)$. When we amplify the power using LC circuit with $Q$ value, the signal to noise ratio is $4.5\times 10^4(Q/10^6)(B/5\mbox{T})^2(t_{obs}/1\sec)^{1/2}\,(10^{-5}\mbox{eV}/m_a) (L/10\mbox{cm})^2(\sigma/3.3\times 10^7\rm eV)$ with $t_{obs}$ observational time.